Open differential:Force at the planetary wheel

[marellasunny]

http://imageshack.com/a/img33/5853/ge7y.gif

In the above diagram,the part 3 the planetary wheel(its not the gear at the input or output side but in the middle of the differential). I call it the planetary wheel because I consider a bevel gear differential just an approximation of a planteary gear differential with equal radii of ring and sun gears. First of all,I want to clarify:

1.A open differential transfers equal power to the left and right wheels,right? P_left=P_right
I make this presumption because when taking a turn,the angular velocities of the wheel are different and hence to make the power equal,I would need to vary the torques.I mean:
M_left * ω_left =M_right *ω_right

So,if
ω_left<ω_right => M_left > M_right

Am I right with this logic?

2. If the above logic is correct, in the above diagram the force [F_E /2] would vary at the left and right wheels. If [F_E/2] were equal,the planetary gears would revolve and not rotate around their axis(straight line driving). But,in case of the turns, what would the force magnitude at the planetary wheel be(marked with a question mark in above diagr.)? I presume this would be [F_left-F_right]. Am I correct?

 

[jack action]

No, P_left ≠ P_right.

But T_left = T_right, no matter what.

From http://zhome.com/ZCMnL/tech/Torsen/Torsen.htm:

The drive axles associated with an open differential are interconnected by a bevel gear set designed to divide equal torque between drive axles. This arrangement will not support any substantial torque difference between the drive axles and, as a consequence, offers very little resistance to differentiation. Virtually any attempt to deliver an increased amount of torque to one of the drive axles will result in rotation of the gear set as evidenced by differential rotation between drive axles. For example, if one of the drive wheels should lose traction, any attempt to deliver additional torque to the other drive wheel having better traction will result in undesirable 'spin up' of the wheel having poorer traction. The maximum amount of torque conveyed by the drive axles collectively is limited to approximately twice the amount of torque supported by the drive wheel having the least traction.

Thought experiment: It is possible to have one wheel rotating on an ice patch while the other is not rotating because it is on asphalt. If one wheel has 0 rpm, then it must have no power (P = Tω), hence -obviously - it cannot have the same power as the other wheel.